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19  Machine Learning

19.1 Getting Started

19.1.1 Load Packages

library("petersenlab")
library("parallel")
library("doParallel")
library("missRanger")
library("powerjoin")
library("caret")
library("gpboost")
library("tidyverse")

19.1.2 Load Data

# Downloaded Data - Processed
load(file = "./data/nfl_players.RData")
load(file = "./data/nfl_teams.RData")
load(file = "./data/nfl_rosters.RData")
load(file = "./data/nfl_rosters_weekly.RData")
load(file = "./data/nfl_schedules.RData")
load(file = "./data/nfl_combine.RData")
load(file = "./data/nfl_draftPicks.RData")
load(file = "./data/nfl_depthCharts.RData")
load(file = "./data/nfl_pbp.RData")
load(file = "./data/nfl_4thdown.RData")
load(file = "./data/nfl_participation.RData")
#load(file = "./data/nfl_actualFantasyPoints_weekly.RData")
load(file = "./data/nfl_injuries.RData")
load(file = "./data/nfl_snapCounts.RData")
load(file = "./data/nfl_espnQBR_seasonal.RData")
load(file = "./data/nfl_espnQBR_weekly.RData")
load(file = "./data/nfl_nextGenStats_weekly.RData")
load(file = "./data/nfl_advancedStatsPFR_seasonal.RData")
load(file = "./data/nfl_advancedStatsPFR_weekly.RData")
load(file = "./data/nfl_playerContracts.RData")
load(file = "./data/nfl_ftnCharting.RData")
load(file = "./data/nfl_playerIDs.RData")
load(file = "./data/nfl_rankings_draft.RData")
load(file = "./data/nfl_rankings_weekly.RData")
load(file = "./data/nfl_expectedFantasyPoints_weekly.RData")
load(file = "./data/nfl_expectedFantasyPoints_pbp.RData")

# Calculated Data - Processed
load(file = "./data/nfl_actualStats_career.RData")
load(file = "./data/nfl_actualStats_seasonal.RData")
load(file = "./data/player_stats_weekly.RData")
load(file = "./data/player_stats_seasonal.RData")

19.1.3 Specify Options

options(scipen = 999) # prevent scientific notation

19.2 Overview of Machine Learning

Machine learning takes us away from focusing on causal inference. Machine learning does not care about which processes are causal—i.e., which processes influence the outcome. Instead, machine learning cares about prediction—it cares about a predictor variable to the extent that it increases predictive accuracy regardless of whether it is causally related to the outcome.

Machine learning can be useful for leveraging big data and lots of predictor variable to develop predictive models with greater accuracy. However, many machine learning techniques are black boxes—it is often unclear how or why certain predictions are made, which can make it difficult to interpret the model’s decisions and understand the underlying relationships between variables. Machine learning tends to be a data-driven, atheoretical technique. This can result in overfitting. Thus, when estimating machine learning models, it is common to keep a hold-out sample for use in cross-validation to evaluate the extent of shrinkage of model coefficients. The data that the model is trained on is known as the “training data”. The data that the model was not trained on but is then is independently tested on—i.e., the hold-out sample—is the “test data”. Shrinkage occurs when predictor variables explain some random error variance in the original model. When the model is applied to an independent sample (i.e., the test data), the predictive model will likely not perform quite as well, and the regressions coefficients will tend to get smaller (i.e., shrink).

If the test data were collected as part of the same processes as the original data and were merely held out for purposes of analysis, this is called internal cross-validation. If the test data were collected separately from the original data used to train the model, this is called external cross-validation.

Most machine learning methods were developed with cross-sectional data in mind. That is, they assume that each person has only one observation on the outcome variable. However, with longitudinal data, each person has multiple observations on the outcome variable.

When performing machine learning, various approaches may help address this:

• transform data from long to wide form, so that each person has only one row
• when designing the training and test sets, keep all measurements from the same person in the same data object (either the training or test set); do not have some measurements from a given person in the training set and other measurements from the same person in the test set
• use a machine learning approach that accounts for the clustered/nested nature of the data

19.3 Types of Machine Learning

There are many approaches to machine learning. This chapter discusses several key ones:

• supervised learning
  • continuous outcome (i.e., regression)
    • linear regression
    • lasso regression
    • ridge regression
    • elastic net regression
  • categorical outcome (i.e., classification)
    • logistic regression
    • support vector machine
    • random forest
    • extreme gradient boosting
• unsupervised learning
  • clustering
  • principal component analysis
• semi-supervised learning
• reinforcement learning
  • deep learning
• ensemble

Ensemble machine learning methods combine multiple machine learning approaches with the goal that combining multiple approaches might lead to more accurate predictions that any one method might be able to achieve on its own.

19.3.1 Supervised Learning

[DEFINE SUPERVISED LEARNING]

Unlike linear and logistic regression, various machine learning techniques can handle multicollinearity, including LASSO regression, ridge regression, and elastic net regression. Least absolute shrinkage and selection operator (LASSO) regression helps perform selection of which predictor variables to keep in the model by shrinking some coefficients to zero. Ridge regression shrinks the coefficients of predictor variables toward zero, but not to zero, so it does not perform selection of which predictor variables to retain; this allows it to allow nonzero coefficients for multiple correlated predictor variables in the context of multicollinearity. Elastic net involves a combination of LASSO and ridge regression; it performs selection of which predictor variables to keep by shrinking the coefficients of some predictor variables to zero, and it shrinks the coefficients of some predictor variables toward zero, to address multicollinearity.

Unless interactions or nonlinear terms are specified, linear, logistic, LASSO, ridge, and elastic net regresstion do not account for interactions among the predictor variables or for nonlinear associations between the predictor variables and the outcome variable. By contrast, random forests and extreme gradient boosting do account for interactions among the predictor variables and for nonlinear associations between the predictor variables and the outcome variable.

19.3.2 Unsupervised Learning

[DEFINE UNSUPERVISED LEARNING]

We describe cluster analysis in Chapter 21. We describe principal component analysis in Chapter 23.

19.3.3 Semi-supervised Learning

[DEFINE SEMI-SUPERVISED LEARNING]

19.3.4 Reinforcement Learning

[DEFINE REINFORCEMENT LEARNING]

19.4 Data Processing

19.4.1 Prepare Data for Merging

# Prepare data for merging
#-todo: calculate years_of_experience
## Use common name for the same (gsis_id) ID variable

#nfl_actualFantasyPoints_player_weekly <- nfl_actualFantasyPoints_player_weekly %>% 
#  rename(gsis_id = player_id)
#
#nfl_actualFantasyPoints_player_seasonal <- nfl_actualFantasyPoints_player_seasonal %>% 
#  rename(gsis_id = player_id)

player_stats_seasonal_offense <- player_stats_seasonal %>% 
  filter(position_group %in% c("QB","RB","WR","TE")) %>% 
  rename(gsis_id = player_id)

player_stats_weekly_offense <- player_stats_weekly %>% 
  filter(position_group %in% c("QB","RB","WR","TE")) %>% 
  rename(gsis_id = player_id)

nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>% 
  rename(gsis_id = player_id)

## Rename other variables to ensure common names

## Ensure variables with the same name have the same type
nfl_players <- nfl_players %>% 
  mutate(
    birth_date = as.Date(birth_date),
    jersey_number = as.character(jersey_number),
    gsis_it_id = as.character(gsis_it_id),
    years_of_experience = as.integer(years_of_experience))

player_stats_seasonal_offense <- player_stats_seasonal_offense %>% 
  mutate(
    birth_date = as.Date(birth_date),
    jersey_number = as.character(jersey_number),
    gsis_it_id = as.character(gsis_it_id))

nfl_rosters <- nfl_rosters %>% 
  mutate(
    draft_number = as.integer(draft_number))

nfl_rosters_weekly <- nfl_rosters_weekly %>% 
  mutate(
    draft_number = as.integer(draft_number))

nfl_depthCharts <- nfl_depthCharts %>% 
  mutate(
    season = as.integer(season))

nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>% 
  mutate(
    season = as.integer(season),
    receptions = as.integer(receptions)) %>% 
  distinct(gsis_id, season, week, .keep_all = TRUE) # drop duplicated rows

## Rename variables
nfl_draftPicks <- nfl_draftPicks %>%
  rename(
    games_career = games,
    pass_completions_career = pass_completions,
    pass_attempts_career = pass_attempts,
    pass_yards_career = pass_yards,
    pass_tds_career = pass_tds,
    pass_ints_career = pass_ints,
    rush_atts_career = rush_atts,
    rush_yards_career = rush_yards,
    rush_tds_career = rush_tds,
    receptions_career = receptions,
    rec_yards_career = rec_yards,
    rec_tds_career = rec_tds,
    def_solo_tackles_career = def_solo_tackles,
    def_ints_career = def_ints,
    def_sacks_career = def_sacks
  )

## Subset variables
nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>% 
  select(gsis_id:position, contains("_exp"), contains("_diff"), contains("_team")) #drop "raw stats" variables (e.g., rec_yards_gained) so they don't get coalesced with actual stats

# Check duplicate ids
player_stats_seasonal_offense %>% 
  group_by(gsis_id, season) %>% 
  filter(n() > 1) %>% 
  head()

nfl_advancedStatsPFR_seasonal %>% 
  group_by(gsis_id, season) %>% 
  filter(n() > 1, !is.na(gsis_id)) %>% 
  select(gsis_id, pfr_id, season, team, everything()) %>% 
  head()

Identify objects with shared variable names:

dplyr::intersect(
  names(nfl_players),
  names(nfl_draftPicks))

[1] "gsis_id"  "position"

length(na.omit(nfl_players$position)) # use by default (more cases)

[1] 21360

length(na.omit(nfl_draftPicks$position))

[1] 2855

dplyr::intersect(
  names(player_stats_seasonal_offense),
  names(nfl_advancedStatsPFR_seasonal))

[1] "gsis_id" "season"  "team"    "age"    

length(na.omit(player_stats_seasonal_offense$season)) # use by default (more cases)

[1] 14859

length(na.omit(nfl_advancedStatsPFR_seasonal$season))

[1] 10395

length(na.omit(player_stats_seasonal_offense$team)) # use by default (more cases)

[1] 14858

length(na.omit(nfl_advancedStatsPFR_seasonal$team))

[1] 10395

length(na.omit(player_stats_seasonal_offense$age)) # use by default (more cases)

[1] 14859

length(na.omit(nfl_advancedStatsPFR_seasonal$age))

[1] 10325

dplyr::intersect(
  names(nfl_rosters_weekly),
  names(nfl_expectedFantasyPoints_weekly))

[1] "gsis_id"   "season"    "week"      "position"  "full_name"

length(na.omit(nfl_rosters_weekly$season)) # use by default (more cases)

[1] 845134

length(na.omit(nfl_expectedFantasyPoints_weekly$season))

[1] 100272

length(na.omit(nfl_rosters_weekly$week)) # use by default (more cases)

[1] 841942

length(na.omit(nfl_expectedFantasyPoints_weekly$week))

[1] 100272

length(na.omit(nfl_rosters_weekly$position)) # use by default (more cases)

[1] 845101

length(na.omit(nfl_expectedFantasyPoints_weekly$position))

[1] 97815

length(na.omit(nfl_rosters_weekly$full_name)) # use by default (more cases)

[1] 845118

length(na.omit(nfl_expectedFantasyPoints_weekly$full_name))

[1] 97815

19.4.2 Merge Data

To merge data, we use the powerjoin package (Fabri, 2022):

# Create lists of objects to merge, depending on data structure: id; or id-season; or id-season-week
#-todo: remove redundant variables
playerListToMerge <- list(
  nfl_players %>% filter(!is.na(gsis_id)),
  nfl_draftPicks %>% filter(!is.na(gsis_id)) %>% select(-season)
)

playerSeasonListToMerge <- list(
  player_stats_seasonal_offense %>% filter(!is.na(gsis_id), !is.na(season)),
  nfl_advancedStatsPFR_seasonal %>% filter(!is.na(gsis_id), !is.na(season))
)

playerSeasonWeekListToMerge <- list(
  nfl_rosters_weekly %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week)),
  #nfl_actualStats_offense_weekly,
  nfl_expectedFantasyPoints_weekly %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week))
  #nfl_advancedStatsPFR_weekly,
)

playerSeasonWeekPositionListToMerge <- list(
  nfl_depthCharts %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week))
)

# Merge data
playerMerged <- playerListToMerge %>% 
  reduce(
    powerjoin::power_full_join,
    by = c("gsis_id"),
    conflict = coalesce_xy) # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2

playerSeasonMerged <- playerSeasonListToMerge %>% 
  reduce(
    powerjoin::power_full_join,
    by = c("gsis_id","season"),
    conflict = coalesce_xy) # where the objects have the same variable name (e.g., team), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2

playerSeasonWeekMerged <- playerSeasonWeekListToMerge %>% 
  reduce(
    powerjoin::power_full_join,
    by = c("gsis_id","season","week"),
    conflict = coalesce_xy) # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2

Identify objects with shared variable names:

dplyr::intersect(
  names(playerSeasonMerged),
  names(playerMerged))

 [1] "gsis_id"                  "position"                
 [3] "position_group"           "first_name"              
 [5] "last_name"                "esb_id"                  
 [7] "display_name"             "rookie_year"             
 [9] "college_conference"       "current_team_id"         
[11] "draft_club"               "draft_number"            
[13] "draftround"               "entry_year"              
[15] "football_name"            "gsis_it_id"              
[17] "headshot"                 "jersey_number"           
[19] "short_name"               "smart_id"                
[21] "status"                   "status_description_abbr" 
[23] "status_short_description" "uniform_number"          
[25] "height"                   "weight"                  
[27] "college_name"             "birth_date"              
[29] "suffix"                   "years_of_experience"     
[31] "pfr_player_name"          "team"                    
[33] "age"                     

seasonalData <- powerjoin::power_full_join(
  playerSeasonMerged,
  playerMerged %>% select(-age, -years_of_experience, -team, -team_abbr, -team_seq, -current_team_id), # drop variables from id objects that change from year to year (and thus are not necessarily accurate for a given season)
  by = "gsis_id",
  conflict = coalesce_xy # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2
) %>% 
  filter(!is.na(season)) %>% 
  select(gsis_id, season, player_display_name, position, team, games, everything())

dplyr::intersect(
  names(playerSeasonWeekMerged),
  names(seasonalData))

 [1] "gsis_id"                 "season"                 
 [3] "week"                    "team"                   
 [5] "jersey_number"           "status"                 
 [7] "first_name"              "last_name"              
 [9] "birth_date"              "height"                 
[11] "weight"                  "college"                
[13] "pfr_id"                  "headshot_url"           
[15] "status_description_abbr" "football_name"          
[17] "esb_id"                  "gsis_it_id"             
[19] "smart_id"                "entry_year"             
[21] "rookie_year"             "draft_club"             
[23] "draft_number"            "position"               

seasonalAndWeeklyData <- powerjoin::power_full_join(
  playerSeasonWeekMerged,
  seasonalData,
  by = c("gsis_id","season"),
  conflict = coalesce_xy # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2
) %>% 
  filter(!is.na(week)) %>% 
  select(gsis_id, season, week, full_name, position, team, everything())

# Duplicate cases
seasonalData %>% 
  group_by(gsis_id, season) %>% 
  filter(n() > 1) %>% 
  head()

seasonalAndWeeklyData %>% 
  group_by(gsis_id, season, week) %>% 
  filter(n() > 1) %>% 
  head()

19.4.3 Additional Processing

# Convert character and logical variables to factors
seasonalData <- seasonalData %>% 
  mutate(
    across(
      where(is.character),
      as.factor
    ),
    across(
      where(is.logical),
      as.factor
    )
  )

19.4.4 Fill in Missing Data for Static Variables

seasonalData <- seasonalData %>% 
  arrange(gsis_id, season) %>% 
  group_by(gsis_id) %>% 
  fill(
    player_name, player_display_name, pos, position, position_group,
    .direction = "downup") %>% 
  ungroup()

19.4.5 Lag Fantasy Points

seasonalData_lag <- seasonalData %>% 
  arrange(gsis_id, season) %>% 
  group_by(gsis_id) %>% 
  mutate(
    fantasyPoints_lag = lead(fantasyPoints)
  ) %>% 
  ungroup()

seasonalData_lag %>% 
  select(gsis_id, player_display_name, season, fantasyPoints, fantasyPoints_lag) # verify that lagging worked as expected

19.4.6 Subset to Predictor Variables and Outcome Variable

seasonalData_lag %>% select_if(~class(.) == "Date")

seasonalData_lag %>% select_if(is.character)

seasonalData_lag %>% select_if(is.factor)

seasonalData_lag %>% select_if(is.logical)

dropVars <- c(
  "birth_date", "loaded", "full_name", "player_name", "player_display_name", "display_name", "suffix", "headshot_url", "player", "pos",
  "espn_id", "sportradar_id", "yahoo_id", "rotowire_id", "pff_id", "fantasy_data_id", "sleeper_id", "pfr_id",
  "pfr_player_id", "cfb_player_id", "pfr_player_name", "esb_id", "gsis_it_id", "smart_id",
  "college", "college_name", "team_abbr", "current_team_id", "college_conference", "draft_club", "status_description_abbr",
  "status_short_description", "short_name", "headshot", "uniform_number", "jersey_number", "first_name", "last_name",
  "football_name", "team")

seasonalData_lag_subset <- seasonalData_lag %>% 
  dplyr::select(-any_of(dropVars))

19.4.7 Separate by Position

seasonalData_lag_subsetQB <- seasonalData_lag_subset %>% 
  filter(position == "QB") %>% 
  select(
    gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
    height, weight, rookie_year, draft_number,
    fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
    completions:rushing_2pt_conversions, special_teams_tds, contains(".pass"), contains(".rush"))

seasonalData_lag_subsetRB <- seasonalData_lag_subset %>% 
  filter(position == "RB") %>% 
  select(
    gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
    height, weight, rookie_year, draft_number,
    fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
    carries:special_teams_tds, contains(".rush"), contains(".rec"))

seasonalData_lag_subsetWR <- seasonalData_lag_subset %>% 
  filter(position == "WR") %>% 
  select(
    gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
    height, weight, rookie_year, draft_number,
    fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
    carries:special_teams_tds, contains(".rush"), contains(".rec"))

seasonalData_lag_subsetTE <- seasonalData_lag_subset %>% 
  filter(position == "TE") %>% 
  select(
    gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
    height, weight, rookie_year, draft_number,
    fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
    carries:special_teams_tds, contains(".rush"), contains(".rec"))

19.4.8 Split into Test and Training Data

seasonalData_lag_qb_all <- seasonalData_lag_subsetQB
seasonalData_lag_rb_all <- seasonalData_lag_subsetRB
seasonalData_lag_wr_all <- seasonalData_lag_subsetWR
seasonalData_lag_te_all <- seasonalData_lag_subsetTE

set.seed(52242) # for reproducibility (to keep the same train/holdout players)

activeQBs <- unique(seasonalData_lag_qb_all$gsis_id[which(seasonalData_lag_qb_all$season == max(seasonalData_lag_qb_all$season, na.rm = TRUE))])
retiredQBs <- unique(seasonalData_lag_qb_all$gsis_id[which(seasonalData_lag_qb_all$gsis_id %ni% activeQBs)])
numQBs <- length(unique(seasonalData_lag_qb_all$gsis_id))
qbHoldoutIDs <- sample(retiredQBs, size = ceiling(.2 * numQBs)) # holdout 20% of players

activeRBs <- unique(seasonalData_lag_rb_all$gsis_id[which(seasonalData_lag_rb_all$season == max(seasonalData_lag_rb_all$season, na.rm = TRUE))])
retiredRBs <- unique(seasonalData_lag_rb_all$gsis_id[which(seasonalData_lag_rb_all$gsis_id %ni% activeRBs)])
numRBs <- length(unique(seasonalData_lag_rb_all$gsis_id))
rbHoldoutIDs <- sample(retiredRBs, size = ceiling(.2 * numRBs)) # holdout 20% of players

set.seed(52242) # for reproducibility (to keep the same train/holdout players); added here to prevent a downstream error with predict.missRanger() due to missingness; this suggests that an error can arise from including a player in the holdout sample who has missingness in particular variables; would be good to identify which player(s) in the holdout sample evoke that error to identify the kinds of missingness that yield the error

activeWRs <- unique(seasonalData_lag_wr_all$gsis_id[which(seasonalData_lag_wr_all$season == max(seasonalData_lag_wr_all$season, na.rm = TRUE))])
retiredWRs <- unique(seasonalData_lag_wr_all$gsis_id[which(seasonalData_lag_wr_all$gsis_id %ni% activeWRs)])
numWRs <- length(unique(seasonalData_lag_wr_all$gsis_id))
wrHoldoutIDs <- sample(retiredWRs, size = ceiling(.2 * numWRs)) # holdout 20% of players

activeTEs <- unique(seasonalData_lag_te_all$gsis_id[which(seasonalData_lag_te_all$season == max(seasonalData_lag_te_all$season, na.rm = TRUE))])
retiredTEs <- unique(seasonalData_lag_te_all$gsis_id[which(seasonalData_lag_te_all$gsis_id %ni% activeTEs)])
numTEs <- length(unique(seasonalData_lag_te_all$gsis_id))
teHoldoutIDs <- sample(retiredTEs, size = ceiling(.2 * numTEs)) # holdout 20% of players
  
seasonalData_lag_qb_train <- seasonalData_lag_qb_all %>% 
  filter(gsis_id %ni% qbHoldoutIDs)
seasonalData_lag_qb_test <- seasonalData_lag_qb_all %>% 
  filter(gsis_id %in% qbHoldoutIDs)

seasonalData_lag_rb_train <- seasonalData_lag_rb_all %>% 
  filter(gsis_id %ni% rbHoldoutIDs)
seasonalData_lag_rb_test <- seasonalData_lag_rb_all %>% 
  filter(gsis_id %in% rbHoldoutIDs)

seasonalData_lag_wr_train <- seasonalData_lag_wr_all %>% 
  filter(gsis_id %ni% wrHoldoutIDs)
seasonalData_lag_wr_test <- seasonalData_lag_wr_all %>% 
  filter(gsis_id %in% wrHoldoutIDs)

seasonalData_lag_te_train <- seasonalData_lag_te_all %>% 
  filter(gsis_id %ni% teHoldoutIDs)
seasonalData_lag_te_test <- seasonalData_lag_te_all %>% 
  filter(gsis_id %in% teHoldoutIDs)

19.4.9 Impute the Missing Data

Here is a vignette demonstrating how to impute missing data using missForest(): https://rpubs.com/lmorgan95/MissForest (archived at: https://perma.cc/6GB4-2E22). Below, we impute the training data (and all data) separately by position. We then use the imputed training data to make out-of-sample predictions to fill in the missing data for the testing data. We do not want to impute the training and testing data together so that we can keep them separate for the purposes of cross-validation. However, we impute all data (training and test data together) for purposes of making out-of-sample predictions from the machine learning models to predict players’ performance next season (when actuals are not yet available for evaluating their accuracy). To impute data, we use the missRanger package (Mayer, 2024).

Note 19.1: Impute missing data for machine learning

Note: the following code takes a while to run.

# QBs
seasonalData_lag_qb_all_imp <- missRanger::missRanger(
  seasonalData_lag_qb_all,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        fantasy_points, fantasy_points_ppr, special_teams_tds, passing_epa, pacr, rushing_epa, fantasyPoints_lag, passing_cpoe, rookie_year, draft_number, gs, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, pocket_time.pass
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, completions, attempts, passing_yards, passing_tds, passing_interceptions, sacks_suffered, sack_yards_lost, sack_fumbles, sack_fumbles_lost, passing_air_yards, passing_yards_after_catch, passing_first_downs, passing_epa, passing_cpoe, passing_2pt_conversions, pacr, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, special_teams_tds, pocket_time.pass, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush

    fntsy_  fnts__  spcl__  pssng_p pacr    rshng_  fntsP_  pssng_c rok_yr  drft_n  gs  pss_t.  thrww.  spks.p  drps.p  bd_th.  tms_b.  tms_hr. tms_ht. tms_p.  bttd_.  on_tgt_t.   rp_pl.  rp_yr.  rp_pss_t.   rp_pss_y.   rp_rsh_t.   rp_rsh_y.   p_pss_t.    p_pss_y.    att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_t.  att_b.  drp_p.  bd_t_.  on_tgt_p.   prss_.  ybc_t.  yc_tt.  pckt_.
iter 1: 0.0054  0.0024  0.7924  0.1919  0.7612  0.3628  0.4789  0.4133  0.0224  0.5216  0.0271  0.0134  0.3024  0.7659  0.1304  0.0541  0.0758  0.1759  0.1820  0.0370  0.3238  0.0291  0.2952  0.1812  0.0885  0.0867  0.2627  0.2563  0.1093  0.0902  0.0580  0.0645  0.1732  0.0524  0.0578  0.1795  0.3524  0.3428  0.7447  0.5158  0.0824  0.6803  0.3529  0.5758  0.8111  
iter 2: 0.0044  0.0048  0.8304  0.2002  0.7926  0.3736  0.4801  0.4289  0.0488  0.6139  0.0188  0.0090  0.2883  0.7481  0.0764  0.0385  0.0718  0.1231  0.1329  0.0337  0.2760  0.0113  0.0548  0.0814  0.0765  0.0990  0.1989  0.2841  0.0707  0.0952  0.0396  0.0386  0.1606  0.0492  0.0525  0.1220  0.2541  0.3556  0.7468  0.4937  0.0827  0.6610  0.3465  0.5796  0.8134  
iter 3: 0.0049  0.0046  0.8690  0.1986  0.7810  0.3641  0.4774  0.4360  0.0528  0.6123  0.0188  0.0088  0.2867  0.7538  0.0767  0.0393  0.0734  0.1261  0.1374  0.0343  0.2741  0.0119  0.0524  0.0816  0.0748  0.1008  0.2184  0.2811  0.0691  0.0926  0.0389  0.0413  0.1640  0.0511  0.0585  0.1255  0.2510  0.3609  0.7477  0.5108  0.0858  0.6426  0.3588  0.5734  0.8300  

seasonalData_lag_qb_all_imp

missRanger object. Extract imputed data via $data
- best iteration: 2 
- best average OOB imputation error: 0.2524825 

data_all_qb <- seasonalData_lag_qb_all_imp$data
data_all_qb$fantasyPointsMC_lag <- scale(data_all_qb$fantasyPoints_lag, scale = FALSE) # mean-centered
data_all_qb_matrix <- data_all_qb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()
newData_qb <- data_all_qb %>% 
  filter(season == max(season, na.rm = TRUE)) %>% 
  select(-fantasyPoints_lag, -fantasyPointsMC_lag)
newData_qb_matrix <- data_all_qb_matrix[
  data_all_qb_matrix[, "season"] == max(data_all_qb_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
  , # all columns
  drop = FALSE]

dropCol_qb <- which(colnames(newData_qb_matrix) %in% c("fantasyPoints_lag","fantasyPointsMC_lag"))
newData_qb_matrix <- newData_qb_matrix[, -dropCol_qb, drop = FALSE]

seasonalData_lag_qb_train_imp <- missRanger::missRanger(
  seasonalData_lag_qb_train,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        fantasy_points, fantasy_points_ppr, special_teams_tds, passing_epa, pacr, rushing_epa, fantasyPoints_lag, passing_cpoe, rookie_year, draft_number, gs, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, pocket_time.pass
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, completions, attempts, passing_yards, passing_tds, passing_interceptions, sacks_suffered, sack_yards_lost, sack_fumbles, sack_fumbles_lost, passing_air_yards, passing_yards_after_catch, passing_first_downs, passing_epa, passing_cpoe, passing_2pt_conversions, pacr, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, special_teams_tds, pocket_time.pass, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush

    fntsy_  fnts__  spcl__  pssng_p pacr    rshng_  fntsP_  pssng_c rok_yr  drft_n  gs  pss_t.  thrww.  spks.p  drps.p  bd_th.  tms_b.  tms_hr. tms_ht. tms_p.  bttd_.  on_tgt_t.   rp_pl.  rp_yr.  rp_pss_t.   rp_pss_y.   rp_rsh_t.   rp_rsh_y.   p_pss_t.    p_pss_y.    att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_t.  att_b.  drp_p.  bd_t_.  on_tgt_p.   prss_.  ybc_t.  yc_tt.  pckt_.
iter 1: 0.0061  0.0028  0.8162  0.1897  0.5083  0.3633  0.4726  0.4456  0.0242  0.4723  0.0283  0.0141  0.2939  0.7728  0.1343  0.0558  0.0744  0.1757  0.1818  0.0381  0.3288  0.0351  0.2921  0.1846  0.0860  0.0894  0.2737  0.2661  0.1127  0.0900  0.0586  0.0644  0.1800  0.0574  0.0639  0.1792  0.3570  0.3486  0.7646  0.5313  0.0868  0.7084  0.3533  0.5933  0.8466  
iter 2: 0.0052  0.0052  0.8304  0.1937  0.5621  0.3715  0.4614  0.4586  0.0505  0.5647  0.0192  0.0092  0.2953  0.7530  0.0800  0.0393  0.0725  0.1170  0.1355  0.0343  0.2771  0.0121  0.0555  0.0731  0.0713  0.0979  0.2073  0.2943  0.0698  0.0911  0.0416  0.0399  0.1683  0.0527  0.0577  0.1262  0.2474  0.3582  0.7719  0.5165  0.0900  0.6862  0.3642  0.5926  0.8400  
iter 3: 0.0053  0.0051  0.8261  0.2008  0.5551  0.3571  0.4727  0.4410  0.0551  0.5658  0.0188  0.0092  0.2859  0.7460  0.0807  0.0402  0.0739  0.1202  0.1393  0.0351  0.2808  0.0114  0.0595  0.0705  0.0775  0.1051  0.2163  0.2935  0.0718  0.0921  0.0426  0.0400  0.1719  0.0535  0.0534  0.1225  0.2498  0.3484  0.7502  0.5100  0.0884  0.6609  0.3672  0.5852  0.8440  
iter 4: 0.0054  0.0051  0.6928  0.1979  0.5598  0.3732  0.4771  0.4349  0.0506  0.5691  0.0189  0.0085  0.2891  0.7456  0.0785  0.0395  0.0737  0.1210  0.1353  0.0335  0.2836  0.0117  0.0566  0.0778  0.0743  0.1055  0.2131  0.2964  0.0697  0.0912  0.0396  0.0395  0.1611  0.0531  0.0597  0.1258  0.2600  0.3560  0.8062  0.5032  0.0973  0.6739  0.3698  0.5875  0.8485  
iter 5: 0.0052  0.0055  0.8355  0.1965  0.5664  0.3710  0.4743  0.4604  0.0520  0.5598  0.0193  0.0091  0.2852  0.7474  0.0800  0.0405  0.0722  0.1213  0.1366  0.0344  0.2788  0.0118  0.0555  0.0756  0.0746  0.0986  0.2190  0.2765  0.0695  0.0932  0.0390  0.0425  0.1650  0.0509  0.0576  0.1305  0.2556  0.3509  0.7738  0.5051  0.0969  0.6902  0.3640  0.6007  0.8326  

seasonalData_lag_qb_train_imp

missRanger object. Extract imputed data via $data
- best iteration: 4 
- best average OOB imputation error: 0.2482278 

data_train_qb <- seasonalData_lag_qb_train_imp$data
data_train_qb$fantasyPointsMC_lag <- scale(data_train_qb$fantasyPoints_lag, scale = FALSE) # mean-centered
data_train_qb_matrix <- data_train_qb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

seasonalData_lag_qb_test_imp <- predict(
  object = seasonalData_lag_qb_train_imp,
  newdata = seasonalData_lag_qb_test,
  seed = 52242)

data_test_qb <- seasonalData_lag_qb_test_imp
data_test_qb_matrix <- data_test_qb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

# RBs
seasonalData_lag_rb_all_imp <- missRanger::missRanger(
  seasonalData_lag_rb_all,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, rushing_epa, air_yards_share, receiving_epa, racr, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, ybc_att.rush, yac_att.rush, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    games   agCn20  agC20Q  fntsy_  fnts__  fntsyP  carris  rshng_y rshng_t rshng_f rshng_fm_   rshng_fr_   rsh_2_  rcptns  targts  rcvng_y rcvng_t rcvng_f rcvng_fm_   rcvng_r_    rcv___  rcvng_fr_   rcv_2_  spcl__  yrs_f_  rshng_p ar_yr_  rcvng_p racr    trgt_s  wopr    fntsP_  rok_yr  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  ybc_t.  yc_tt.  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r
iter 1: 0.8865  0.0057  0.0031  0.4544  0.0178  0.0032  0.0745  0.0233  0.1462  0.4895  0.2594  0.0295  0.9849  0.0690  0.0666  0.0534  0.4327  0.8626  0.4824  0.6841  0.0322  0.0614  1.0171  0.8263  0.1817  0.4512  0.3321  0.3894  0.5211  0.4549  0.1817  0.5440  0.0197  0.5999  0.1700  0.0244  0.0222  0.0792  0.0297  0.0527  0.0520  0.2134  0.3431  0.0252  0.0180  0.0257  0.1634  0.0437  0.3108  0.0217  0.3925  0.4610  0.6941  0.4880  0.5402  0.2670  0.2026  0.3482  0.1596  0.2698  0.3637  
iter 2: 0.2755  0.0162  0.0207  0.0063  0.0037  0.0044  0.0161  0.0148  0.0912  0.2524  0.2898  0.0248  0.9832  0.0273  0.0444  0.0233  0.2065  0.4600  0.4891  0.1285  0.0332  0.0457  1.0175  0.8566  0.1824  0.4212  0.2329  0.3099  0.5605  0.2569  0.1742  0.5373  0.0424  0.6377  0.1653  0.0167  0.0123  0.0859  0.0302  0.0367  0.0349  0.1030  0.3689  0.0144  0.0159  0.0195  0.1403  0.0434  0.1549  0.0190  0.3840  0.1050  0.5453  0.4882  0.5616  0.2472  0.1953  0.1525  0.1687  0.2595  0.3619  
iter 3: 0.2744  0.0163  0.0231  0.0062  0.0038  0.0047  0.0152  0.0137  0.0980  0.2601  0.2906  0.0244  0.9800  0.0265  0.0347  0.0231  0.2101  0.4638  0.4954  0.1284  0.0283  0.0458  1.0114  0.8731  0.1818  0.4117  0.2278  0.3037  0.5699  0.2052  0.1800  0.5389  0.0400  0.6423  0.1624  0.0166  0.0124  0.0893  0.0306  0.0374  0.0356  0.1074  0.3628  0.0144  0.0163  0.0187  0.1390  0.0463  0.1583  0.0190  0.3882  0.1062  0.5642  0.4796  0.5570  0.2380  0.1935  0.1586  0.1588  0.2625  0.3648  
iter 4: 0.2776  0.0169  0.0220  0.0063  0.0038  0.0045  0.0151  0.0138  0.0979  0.2584  0.2846  0.0243  0.9782  0.0263  0.0281  0.0221  0.1968  0.4594  0.4817  0.1267  0.0290  0.0462  1.0104  0.8614  0.1854  0.4216  0.2333  0.3004  0.5467  0.1917  0.1815  0.5353  0.0443  0.6503  0.1657  0.0166  0.0121  0.0905  0.0313  0.0378  0.0357  0.1041  0.3437  0.0155  0.0159  0.0185  0.1405  0.0441  0.1613  0.0196  0.3816  0.1117  0.5682  0.5011  0.5585  0.2421  0.1975  0.1520  0.1770  0.2650  0.3647  
iter 5: 0.2752  0.0163  0.0226  0.0063  0.0038  0.0045  0.0158  0.0138  0.1015  0.2614  0.2857  0.0242  0.9740  0.0250  0.0303  0.0218  0.2004  0.4607  0.4810  0.1167  0.0285  0.0449  1.0077  0.8658  0.1835  0.4182  0.2170  0.2995  0.5690  0.2010  0.1794  0.5375  0.0385  0.6487  0.1652  0.0166  0.0124  0.0878  0.0306  0.0368  0.0353  0.1069  0.3539  0.0154  0.0159  0.0193  0.1409  0.0447  0.1598  0.0205  0.3873  0.1062  0.5583  0.4895  0.5501  0.2418  0.1979  0.1713  0.1726  0.2625  0.3596  
iter 6: 0.2760  0.0158  0.0223  0.0063  0.0037  0.0046  0.0150  0.0144  0.0982  0.2568  0.2816  0.0238  0.9810  0.0253  0.0273  0.0223  0.2141  0.4606  0.4881  0.1386  0.0300  0.0457  1.0174  0.8605  0.1821  0.4188  0.2263  0.2985  0.5497  0.1779  0.1536  0.5388  0.0389  0.6422  0.1668  0.0162  0.0119  0.0897  0.0305  0.0376  0.0356  0.1066  0.3529  0.0149  0.0159  0.0196  0.1446  0.0450  0.1585  0.0197  0.3857  0.1001  0.5607  0.4948  0.5478  0.2487  0.1945  0.1438  0.1543  0.2568  0.3612  
iter 7: 0.2748  0.0158  0.0212  0.0064  0.0039  0.0047  0.0149  0.0141  0.0986  0.2611  0.2877  0.0241  0.9755  0.0253  0.0310  0.0223  0.2163  0.4553  0.4885  0.1335  0.0293  0.0456  1.0096  0.8575  0.1821  0.4236  0.2203  0.2998  0.5510  0.2107  0.1797  0.5354  0.0416  0.6395  0.1646  0.0166  0.0117  0.0895  0.0310  0.0371  0.0361  0.1073  0.3547  0.0154  0.0156  0.0193  0.1410  0.0449  0.1628  0.0201  0.3892  0.1076  0.5609  0.4946  0.5643  0.2392  0.1899  0.1540  0.1423  0.2667  0.3603  

seasonalData_lag_rb_all_imp

missRanger object. Extract imputed data via $data
- best iteration: 6 
- best average OOB imputation error: 0.2175486 

data_all_rb <- seasonalData_lag_rb_all_imp$data
data_all_rb$fantasyPointsMC_lag <- scale(data_all_rb$fantasyPoints_lag, scale = FALSE) # mean-centered
data_all_rb_matrix <- data_all_rb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()
newData_rb <- data_all_rb %>% 
  filter(season == max(season, na.rm = TRUE)) %>% 
  select(-fantasyPoints_lag, -fantasyPointsMC_lag)
newData_rb_matrix <- data_all_rb_matrix[
  data_all_rb_matrix[, "season"] == max(data_all_rb_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
  , # all columns
  drop = FALSE]

dropCol_rb <- which(colnames(newData_rb_matrix) %in% c("fantasyPoints_lag","fantasyPointsMC_lag"))
newData_rb_matrix <- newData_rb_matrix[, -dropCol_rb, drop = FALSE]

seasonalData_lag_rb_train_imp <- missRanger::missRanger(
  seasonalData_lag_rb_train,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, rushing_epa, air_yards_share, receiving_epa, racr, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, ybc_att.rush, yac_att.rush, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    games   agCn20  agC20Q  fntsy_  fnts__  fntsyP  carris  rshng_y rshng_t rshng_f rshng_fm_   rshng_fr_   rsh_2_  rcptns  targts  rcvng_y rcvng_t rcvng_f rcvng_fm_   rcvng_r_    rcv___  rcvng_fr_   rcv_2_  spcl__  yrs_f_  rshng_p ar_yr_  rcvng_p racr    trgt_s  wopr    fntsP_  rok_yr  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  ybc_t.  yc_tt.  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r
iter 1: 0.8759  0.0072  0.0036  0.4578  0.0178  0.0035  0.0736  0.0229  0.1524  0.4776  0.2679  0.0288  0.9965  0.0749  0.0744  0.0553  0.4578  0.8604  0.4998  0.6821  0.0360  0.0639  1.0042  0.8380  0.1806  0.4662  0.3419  0.3961  0.5595  0.4715  0.1968  0.5338  0.0246  0.5882  0.1726  0.0265  0.0235  0.0849  0.0311  0.0550  0.0521  0.2131  0.3689  0.0281  0.0197  0.0286  0.1742  0.0463  0.3114  0.0229  0.3942  0.4806  0.7239  0.5199  0.5631  0.2865  0.2195  0.3630  0.2052  0.2596  0.4091  
iter 2: 0.2745  0.0177  0.0266  0.0067  0.0041  0.0049  0.0169  0.0154  0.1017  0.2590  0.2956  0.0237  0.9814  0.0286  0.0522  0.0240  0.2187  0.4582  0.4919  0.1541  0.0362  0.0475  1.0075  0.8811  0.1822  0.4481  0.2377  0.3184  0.6116  0.2628  0.2007  0.5254  0.0473  0.6411  0.1653  0.0179  0.0132  0.0940  0.0325  0.0392  0.0375  0.1057  0.3678  0.0161  0.0169  0.0196  0.1510  0.0484  0.1521  0.0202  0.3941  0.1035  0.5567  0.5120  0.5666  0.2466  0.2087  0.1733  0.1699  0.2524  0.4066  
iter 3: 0.2766  0.0190  0.0273  0.0067  0.0041  0.0048  0.0159  0.0149  0.0971  0.2615  0.2952  0.0245  0.9668  0.0278  0.0409  0.0240  0.2180  0.4648  0.4931  0.1319  0.0350  0.0495  1.0128  0.8907  0.1820  0.4366  0.2459  0.3124  0.6236  0.2555  0.2114  0.5276  0.0438  0.6314  0.1658  0.0175  0.0122  0.0899  0.0319  0.0386  0.0386  0.1100  0.3783  0.0155  0.0165  0.0194  0.1477  0.0474  0.1499  0.0194  0.3929  0.1121  0.5761  0.5245  0.5651  0.2490  0.2103  0.1767  0.1817  0.2658  0.4106  

seasonalData_lag_rb_train_imp

missRanger object. Extract imputed data via $data
- best iteration: 2 
- best average OOB imputation error: 0.226086 

data_train_rb <- seasonalData_lag_rb_train_imp$data
data_train_rb$fantasyPointsMC_lag <- scale(data_train_rb$fantasyPoints_lag, scale = FALSE) # mean-centered
data_train_rb_matrix <- data_train_rb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

seasonalData_lag_rb_test_imp <- predict(
  object = seasonalData_lag_rb_train_imp,
  newdata = seasonalData_lag_rb_test,
  seed = 52242)

data_test_rb <- seasonalData_lag_rb_test_imp
data_test_rb_matrix <- data_test_rb %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

# WRs
seasonalData_lag_wr_all_imp <- missRanger::missRanger(
  seasonalData_lag_wr_all,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        fantasy_points, fantasy_points_ppr, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, rushing_epa, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, ybc_att.rush, yac_att.rush
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    fntsy_  fnts__  spcl__  yrs_f_  rcvng_  racr    ar_yr_  trgt_s  wopr    fntsP_  rok_yr  rshng_  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r  ybc_t.  yc_tt.
iter 1: 0.0061  0.0010  0.7104  0.1566  0.1040  0.8131  0.1013  0.1722  0.0402  0.4890  0.0150  0.3811  0.6654  0.1459  0.1184  0.0898  0.2353  0.1234  0.0966  0.2670  0.6383  0.3084  0.0198  0.0136  0.0151  0.0671  0.0135  0.0268  0.0442  0.4465  0.4320  0.4674  0.2961  0.1410  0.3819  0.1840  0.2251  0.3929  0.2568  0.4760  
iter 2: 0.0058  0.0019  0.7826  0.1601  0.0835  0.7518  0.0607  0.0930  0.0452  0.4939  0.0296  0.3301  0.6843  0.1440  0.0851  0.0600  0.2638  0.1161  0.0708  0.1804  0.3103  0.3223  0.0109  0.0108  0.0096  0.0719  0.0139  0.0200  0.0318  0.4476  0.0778  0.3692  0.2401  0.1448  0.1629  0.1601  0.2261  0.3793  0.2536  0.4775  
iter 3: 0.0061  0.0019  0.7857  0.1593  0.0829  0.7421  0.0580  0.0986  0.0481  0.4946  0.0318  0.3334  0.6890  0.1430  0.0823  0.0604  0.2595  0.1177  0.0728  0.1802  0.3077  0.3194  0.0109  0.0114  0.0095  0.0724  0.0133  0.0199  0.0312  0.4411  0.0767  0.3687  0.2369  0.1455  0.1530  0.1660  0.2169  0.3878  0.2466  0.4716  
iter 4: 0.0060  0.0018  0.7874  0.1604  0.0832  0.7394  0.0591  0.0940  0.0479  0.4926  0.0301  0.3317  0.6896  0.1434  0.0863  0.0601  0.2562  0.1227  0.0711  0.1900  0.3089  0.3194  0.0105  0.0112  0.0095  0.0707  0.0140  0.0202  0.0318  0.4447  0.0784  0.3674  0.2339  0.1423  0.1592  0.1700  0.2254  0.3886  0.2552  0.4662  

seasonalData_lag_wr_all_imp

missRanger object. Extract imputed data via $data
- best iteration: 3 
- best average OOB imputation error: 0.203846 

data_all_wr <- seasonalData_lag_wr_all_imp$data
data_all_wr$fantasyPointsMC_lag <- scale(data_all_wr$fantasyPoints_lag, scale = FALSE) # mean-centered
data_all_wr_matrix <- data_all_wr %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()
newData_wr <- data_all_wr %>% 
  filter(season == max(season, na.rm = TRUE)) %>% 
  select(-fantasyPoints_lag, -fantasyPointsMC_lag)
newData_wr_matrix <- data_all_wr_matrix[
  data_all_wr_matrix[, "season"] == max(data_all_wr_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
  , # all columns
  drop = FALSE]

dropCol_wr <- which(colnames(newData_wr_matrix) %in% c("fantasyPoints_lag","fantasyPointsMC_lag"))
newData_wr_matrix <- newData_wr_matrix[, -dropCol_wr, drop = FALSE]

seasonalData_lag_wr_train_imp <- missRanger::missRanger(
  seasonalData_lag_wr_train,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        fantasy_points, fantasy_points_ppr, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, rushing_epa, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, ybc_att.rush, yac_att.rush
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    fntsy_  fnts__  spcl__  yrs_f_  rcvng_  racr    ar_yr_  trgt_s  wopr    fntsP_  rok_yr  rshng_  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r  ybc_t.  yc_tt.
iter 1: 0.0064  0.0010  0.7029  0.1611  0.1089  0.8443  0.1021  0.1643  0.0427  0.4935  0.0173  0.3461  0.6788  0.1427  0.1364  0.0993  0.2403  0.1243  0.0979  0.2745  0.6190  0.3171  0.0201  0.0147  0.0159  0.0734  0.0140  0.0280  0.0454  0.4502  0.4439  0.4733  0.3088  0.1641  0.4547  0.2192  0.2439  0.4227  0.2921  0.5068  
iter 2: 0.0063  0.0020  0.7835  0.1630  0.0901  0.8044  0.0674  0.0936  0.0479  0.4930  0.0331  0.3235  0.7090  0.1417  0.0896  0.0659  0.2659  0.1273  0.0752  0.1920  0.3068  0.3225  0.0112  0.0116  0.0101  0.0753  0.0141  0.0210  0.0333  0.4431  0.0809  0.3676  0.2571  0.1617  0.1735  0.1797  0.2441  0.3996  0.2911  0.4923  
iter 3: 0.0063  0.0020  0.7710  0.1639  0.0881  0.7954  0.0646  0.0982  0.0515  0.4956  0.0338  0.3200  0.7088  0.1413  0.0900  0.0640  0.2565  0.1250  0.0735  0.1989  0.3082  0.3280  0.0114  0.0119  0.0096  0.0763  0.0141  0.0216  0.0326  0.4388  0.0807  0.3703  0.2582  0.1623  0.1657  0.2018  0.2375  0.4016  0.2838  0.4794  
iter 4: 0.0062  0.0020  0.7792  0.1625  0.0877  0.8043  0.0632  0.0919  0.0477  0.4963  0.0341  0.3239  0.7038  0.1420  0.0950  0.0653  0.2664  0.1309  0.0767  0.2025  0.2933  0.3076  0.0109  0.0119  0.0097  0.0745  0.0143  0.0217  0.0326  0.4432  0.0804  0.3688  0.2584  0.1605  0.1931  0.2013  0.2378  0.4119  0.2824  0.4860  

seasonalData_lag_wr_train_imp

missRanger object. Extract imputed data via $data
- best iteration: 3 
- best average OOB imputation error: 0.2110456 

data_train_wr <- seasonalData_lag_wr_train_imp$data
data_train_wr$fantasyPointsMC_lag <- scale(data_train_wr$fantasyPoints_lag, scale = FALSE) # mean-centered
data_train_wr_matrix <- data_train_wr %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

seasonalData_lag_wr_test_imp <- predict(
  object = seasonalData_lag_wr_train_imp,
  newdata = seasonalData_lag_wr_test,
  seed = 52242)

data_test_wr <- seasonalData_lag_wr_test_imp
data_test_wr_matrix <- data_test_wr %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

# TEs
seasonalData_lag_te_all_imp <- missRanger::missRanger(
  seasonalData_lag_te_all,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, rushing_epa, ybc_att.rush, yac_att.rush
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    games   agCn20  agC20Q  fntsy_  fnts__  fntsyP  carris  rshng_y rshng_t rshng_f rshng_fm_   rshng_fr_   rsh_2_  rcptns  targts  rcvng_y rcvng_t rcvng_f rcvng_fm_   rcvng_r_    rcv___  rcvng_fr_   rcv_2_  spcl__  yrs_f_  rcvng_p racr    ar_yr_  trgt_s  wopr    fntsP_  rok_yr  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r  rshng_p ybc_t.  yc_tt.
iter 1: 0.8157  0.0061  0.0030  0.3406  0.0194  0.0039  0.5253  0.2259  0.2452  0.7083  0.6874  0.0802  1.1303  0.0281  0.0558  0.0255  0.0845  0.8134  0.4317  0.0655  0.0784  0.0253  0.9716  1.0271  0.1530  0.1689  0.6899  0.1092  0.4432  0.1004  0.4764  0.0180  0.6054  0.3846  0.0762  0.0832  0.1564  0.0618  0.0704  0.2123  0.3921  0.6733  0.0290  0.0207  0.0226  0.1012  0.0212  0.0420  0.0603  0.4332  0.4640  0.4996  0.2804  0.1667  0.3542  0.1652  0.2843  0.3948  0.3270  0.6620  0.7439  
iter 2: 0.1712  0.0175  0.0256  0.0106  0.0037  0.0055  0.1140  0.1113  0.0990  0.5369  0.7422  0.0852  1.1286  0.0193  0.0200  0.0128  0.0862  0.4248  0.4659  0.0206  0.0529  0.0217  0.9711  1.0114  0.1561  0.1397  0.6715  0.0766  0.1819  0.1085  0.4649  0.0366  0.6346  0.3880  0.0722  0.0728  0.1592  0.0680  0.0759  0.2034  0.3651  0.6811  0.0164  0.0158  0.0161  0.1080  0.0211  0.0327  0.0475  0.4342  0.1149  0.4173  0.2589  0.1742  0.1467  0.1531  0.2941  0.3851  0.3357  0.6846  0.7397  
iter 3: 0.1689  0.0170  0.0261  0.0114  0.0040  0.0056  0.1190  0.1155  0.0978  0.6088  0.7899  0.0945  1.1731  0.0195  0.0203  0.0132  0.0964  0.4270  0.4608  0.0202  0.0525  0.0214  0.9694  1.0265  0.1560  0.1380  0.6453  0.0751  0.1794  0.1204  0.4642  0.0364  0.6369  0.3853  0.0779  0.0786  0.1497  0.0569  0.0932  0.2027  0.4003  0.6633  0.0171  0.0164  0.0167  0.1049  0.0220  0.0335  0.0466  0.4371  0.1141  0.4304  0.2665  0.1775  0.1464  0.1537  0.2916  0.3720  0.3137  0.6640  0.7770  

seasonalData_lag_te_all_imp

missRanger object. Extract imputed data via $data
- best iteration: 2 
- best average OOB imputation error: 0.2477098 

data_all_te <- seasonalData_lag_te_all_imp$data
data_all_te$fantasyPointsMC_lag <- scale(data_all_te$fantasyPoints_lag, scale = FALSE) # mean-centered
data_all_te_matrix <- data_all_te %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()
newData_te <- data_all_te %>% 
  filter(season == max(season, na.rm = TRUE)) %>% 
  select(-fantasyPoints_lag, -fantasyPointsMC_lag)
newData_te_matrix <- data_all_te_matrix[
  data_all_te_matrix[, "season"] == max(data_all_te_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
  , # all columns
  drop = FALSE]

dropCol_te <- which(colnames(newData_te_matrix) %in% c("fantasyPoints_lag","fantasyPointsMC_lag"))
newData_te_matrix <- newData_te_matrix[, -dropCol_te, drop = FALSE]

seasonalData_lag_te_train_imp <- missRanger::missRanger(
  seasonalData_lag_te_train,
  pmm.k = 5,
  verbose = 2,
  seed = 52242,
  keep_forests = TRUE)

Variables to impute:        games, years_of_experience, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, rushing_epa, ybc_att.rush, yac_att.rush
Variables used to impute:   gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec

    games   yrs_f_  agCn20  agC20Q  fntsy_  fnts__  fntsyP  carris  rshng_y rshng_t rshng_f rshng_fm_   rshng_fr_   rsh_2_  rcptns  targts  rcvng_y rcvng_t rcvng_f rcvng_fm_   rcvng_r_    rcv___  rcvng_fr_   rcv_2_  spcl__  rcvng_p racr    ar_yr_  trgt_s  wopr    fntsP_  rok_yr  drft_n  gs  att.rs  yds.rs  td.rsh  x1d.rs  ybc.rs  yc.rsh  brk_tkl.rs  att_b.  tgt.rc  rec.rc  yds.rc  td.rec  x1d.rc  ybc.rc  yac.rc  brk_tkl.rc  drp.rc  int.rc  adt.rc  rat.rc  drp_p.  rc_br.  ybc_r.  yc_r.r  rshng_p ybc_t.  yc_tt.
iter 1: 0.8094  0.1093  0.0070  0.0035  0.3272  0.0235  0.0052  0.2840  0.1426  0.2634  0.8628  0.7885  0.0924  1.1067  0.0298  0.0611  0.0249  0.0969  0.8177  0.4537  0.0650  0.0804  0.0249  0.9680  1.0235  0.1738  0.5438  0.0868  0.4123  0.1172  0.4597  0.0189  0.6057  0.3973  0.0877  0.0886  0.1516  0.0467  0.0593  0.2086  0.4018  0.6464  0.0296  0.0223  0.0237  0.1062  0.0207  0.0428  0.0579  0.4367  0.4700  0.4818  0.3045  0.1724  0.4722  0.2410  0.2693  0.4025  0.3943  0.4791  0.7521  
iter 2: 0.1728  0.1469  0.0179  0.0289  0.0104  0.0039  0.0051  0.0863  0.0763  0.1528  0.7880  0.9474  0.0849  1.0234  0.0193  0.0198  0.0137  0.0915  0.4327  0.4835  0.0238  0.0558  0.0221  0.9617  1.0376  0.1464  0.5141  0.0630  0.1827  0.1062  0.4562  0.0379  0.6361  0.3908  0.0641  0.0767  0.1425  0.0603  0.0747  0.1970  0.3903  0.6647  0.0182  0.0171  0.0165  0.1074  0.0226  0.0332  0.0503  0.4361  0.1170  0.4096  0.2673  0.1862  0.2255  0.2386  0.2793  0.4004  0.3648  0.5070  0.7621  
iter 3: 0.1713  0.1447  0.0195  0.0276  0.0104  0.0036  0.0051  0.0796  0.0889  0.1611  0.8505  0.9348  0.0904  1.0447  0.0196  0.0205  0.0134  0.0901  0.4465  0.4867  0.0233  0.0569  0.0222  0.9519  1.0103  0.1457  0.5062  0.0617  0.1698  0.1115  0.4530  0.0382  0.6521  0.3899  0.0665  0.0681  0.1457  0.0647  0.0866  0.2055  0.3919  0.6791  0.0169  0.0169  0.0168  0.1107  0.0213  0.0339  0.0500  0.4315  0.1200  0.4148  0.2745  0.1822  0.1947  0.2205  0.2778  0.4032  0.3639  0.4933  0.7741  

seasonalData_lag_te_train_imp

missRanger object. Extract imputed data via $data
- best iteration: 2 
- best average OOB imputation error: 0.2519559 

data_train_te <- seasonalData_lag_te_train_imp$data
data_train_te$fantasyPointsMC_lag <- scale(data_train_te$fantasyPoints_lag, scale = FALSE) # mean-centered
data_train_te_matrix <- data_train_te %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

seasonalData_lag_te_test_imp <- predict(
  object = seasonalData_lag_te_train_imp,
  newdata = seasonalData_lag_te_test,
  seed = 52242)

data_test_te <- seasonalData_lag_te_test_imp
data_test_te_matrix <- data_test_te %>%
  mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>% 
  as.matrix()

19.5 Identify Cores for Parallel Processing

num_cores <- detectCores() - 1
num_true_cores <- parallel::detectCores(logical = FALSE) - 1

num_cores

[1] 4

19.6 Fitting the Traditional Regression Models

19.6.1 Regression with One Predictor

19.6.2 Regression with Multiple Predictors

19.7 Fitting the Machine Learning Models

19.7.1 Least Absolute Shrinkage and Selection Option (LASSO)

19.7.2 Ridge Regression

19.7.3 Elastic Net

19.7.4 Random Forest Machine Learning

19.7.4.1 Cross-Sectional Data

We use the caret package (Kuhn, 2024). We use the parallel (R-parallel?) and doParallel (Corporation & Weston, 2022) packages for parallel (faster) processing.

cl <- parallel::makeCluster(num_cores)
doParallel::registerDoParallel(cl)

set.seed(52242)

randomForest_qb <- caret::train(
  fantasyPoints_lag ~ ., # use all predictors
  data = seasonalData_lag_subsetQB_imp$ximp,
  method = "rf",
  trControl = trainControl(
    method = "cv",
    number = 10)) # 10-fold cross-validation

Error in eval(expr, p): object 'seasonalData_lag_subsetQB_imp' not found

randomForest_rb <- caret::train(
  fantasyPoints_lag ~ ., # use all predictors
  data = seasonalData_lag_subsetRB_imp$ximp,
  method = "rf",
  trControl = trainControl(
    method = "cv",
    number = 10)) # 10-fold cross-validation

Error in eval(expr, p): object 'seasonalData_lag_subsetRB_imp' not found

randomForest_wr <- caret::train(
  fantasyPoints_lag ~ ., # use all predictors
  data = seasonalData_lag_subsetWR_imp$ximp,
  method = "rf",
  trControl = trainControl(
    method = "cv",
    number = 10)) # 10-fold cross-validation

Error in eval(expr, p): object 'seasonalData_lag_subsetWR_imp' not found

randomForest_te <- caret::train(
  fantasyPoints_lag ~ ., # use all predictors
  data = seasonalData_lag_subsetTE_imp$ximp,
  method = "rf",
  trControl = trainControl(
    method = "cv",
    number = 10)) # 10-fold cross-validation

Error in eval(expr, p): object 'seasonalData_lag_subsetTE_imp' not found

stopCluster(cl)

print(randomForest_qb)

Error: object 'randomForest_qb' not found

print(randomForest_rb)

Error: object 'randomForest_rb' not found

print(randomForest_wr)

Error: object 'randomForest_wr' not found

print(randomForest_te)

Error: object 'randomForest_te' not found

newData_seasonalQB_imp$ximp$fantasyPoints_lag <- predict(
  randomForest_qb,
  newdata = newData_seasonalQB_imp$ximp
)

Error: object 'randomForest_qb' not found

newData_seasonalRB_imp$ximp$fantasyPoints_lag <- predict(
  randomForest_rb,
  newdata = newData_seasonalRB_imp$ximp
)

Error: object 'randomForest_rb' not found

newData_seasonalWR_imp$ximp$fantasyPoints_lag <- predict(
  randomForest_wr,
  newdata = newData_seasonalWR_imp$ximp
)

Error: object 'randomForest_wr' not found

newData_seasonalTE_imp$ximp$fantasyPoints_lag <- predict(
  randomForest_te,
  newdata = newData_seasonalTE_imp$ximp
)

Error: object 'randomForest_te' not found

newData_seasonalQB$fantasyPoints_lag <- newData_seasonalQB_imp$ximp$fantasyPoints_lag

Error: object 'newData_seasonalQB_imp' not found

newData_seasonalRB$fantasyPoints_lag <- newData_seasonalRB_imp$ximp$fantasyPoints_lag

Error: object 'newData_seasonalRB_imp' not found

newData_seasonalWR$fantasyPoints_lag <- newData_seasonalWR_imp$ximp$fantasyPoints_lag

Error: object 'newData_seasonalWR_imp' not found

newData_seasonalTE$fantasyPoints_lag <- newData_seasonalTE_imp$ximp$fantasyPoints_lag

Error: object 'newData_seasonalTE_imp' not found

newData_seasonalQB <- dplyr::left_join(
  newData_seasonalQB,
  newData_seasonal %>% select(gsis_id, player_display_name, team),
  by = "gsis_id"
)

Error: object 'newData_seasonalQB' not found

newData_seasonalRB <- dplyr::left_join(
  newData_seasonalRB,
  newData_seasonal %>% select(gsis_id, player_display_name, team),
  by = "gsis_id"
)

Error: object 'newData_seasonalRB' not found

newData_seasonalWR <- dplyr::left_join(
  newData_seasonalWR,
  newData_seasonal %>% select(gsis_id, player_display_name, team),
  by = "gsis_id"
)

Error: object 'newData_seasonalWR' not found

newData_seasonalTE <- dplyr::left_join(
  newData_seasonalTE,
  newData_seasonal %>% select(gsis_id, player_display_name, team),
  by = "gsis_id"
)

Error: object 'newData_seasonalTE' not found

newData_seasonalQB %>%
  arrange(-fantasyPoints_lag) %>% 
  select(gsis_id, player_display_name, fantasyPoints_lag)

Error: object 'newData_seasonalQB' not found

newData_seasonalRB %>%
  arrange(-fantasyPoints_lag) %>% 
  select(gsis_id, player_display_name, fantasyPoints_lag)

Error: object 'newData_seasonalRB' not found

newData_seasonalWR %>%
  arrange(-fantasyPoints_lag) %>% 
  select(gsis_id, player_display_name, fantasyPoints_lag)

Error: object 'newData_seasonalWR' not found

newData_seasonalTE %>%
  arrange(-fantasyPoints_lag) %>% 
  select(gsis_id, player_display_name, fantasyPoints_lag)

Error: object 'newData_seasonalTE' not found

19.7.4.2 Longitudinal Data

(Hu & Szymczak, 2023)

library("LongituRF")

smerf <- LongituRF::MERF(
  X = seasonalData_subsetQB_imp$ximp[,c("passing_epa")] %>% as.matrix(),
  Y = seasonalData_subsetQB$fantasyPoints_lag,
  Z = seasonalData_subsetQB_imp$ximp[,c("pacr")] %>% as.matrix(),
  id = seasonalData_subsetQB$gsis_id,
  time = seasonalData_subsetQB_imp$ximp[,c("ageCentered20")] %>% as.matrix(),
  ntree = 500,
  sto = "BM")

smerf$forest # the fitted random forest (obtained at the last iteration)
smerf$random_effects # the predicted random effects for each player
smerf$omega # the predicted stochastic processes
plot(smerf$Vraisemblance) # evolution of the log-likelihood
smerf$OOB # OOB error at each iteration

19.7.5 k-Fold Cross-Validation

19.7.6 Leave-One-Out (LOO) Cross-Validation

19.7.7 Combining Tree-Boosting with Mixed Models

To combine tree-boosting with mixed models, we use the gpboost package (gpboost?).

Adapted from here: https://towardsdatascience.com/mixed-effects-machine-learning-for-longitudinal-panel-data-with-gpboost-part-iii-523bb38effc

19.7.7.1 Process Data

If using a gamma distribution, it requires positive-only values:

data_train_qb_matrix[,"fantasyPoints_lag"][data_train_qb_matrix[,"fantasyPoints_lag"] <= 0] <- 0.01

19.7.7.2 Specify Predictor Variables

pred_vars_qb <- data_train_qb_matrix %>% 
  as_tibble() %>% 
  select(-fantasyPoints_lag, -fantasyPointsMC_lag, -ageCentered20, ageCentered20Quadratic) %>% # -gsis_id
  names()

pred_vars_qb_categorical <- "gsis_id" # to specify categorical predictors

19.7.7.3 Specify General Model Options

model_likelihood <- "gamma" # gaussian
nrounds <- 2000 # maximum number of boosting iterations (i.e., number of trees built sequentially); more rounds = potentially better learning, but also greater risk of overfitting

19.7.7.4 Identify Optimal Tuning Parameters

For identifying the optimal tuning parameters for boosting, we partition the training data into inner training data and validation data. We randomly split the training data into 80% inner training data and 20% held-out validation data. We then use the mean absolute error as our index of prediction accuracy on the held-out validation data.

# Partition training data into inner training data and validation data
ntrain_qb <- dim(data_train_qb_matrix)[1]

set.seed(52242)
valid_tune_idx_qb <- sample.int(ntrain_qb, as.integer(0.2*ntrain_qb)) # 

folds_qb <- list(valid_tune_idx_qb)

# Specify parameter grid, gp_model, and gpb.Dataset
param_grid_qb <- list(
  "learning_rate" = c(0.2, 0.1, 0.05, 0.01), # the step size used when updating predictions after each boosting round (high values make big updates, which can speed up learning but risk overshooting; low values are usually more accurate but require more rounds)
  "max_depth" = c(3, 5, 7), # maximum depth (levels) of each decision tree; deeper trees capture more complex patterns and interactions but risk overfitting; shallower trees tend to generalize better
  "min_data_in_leaf" = c(10, 50, 100), # minimum number of training examples in a leaf node; higher values = more regularization (simpler trees)
  "lambda_l2" = c(0, 1, 5)) # L2 regularization penalty for large weights in tree splits; adds a "cost" for complexity; helps prevent overfitting by shrinking the contribution of each tree

other_params_qb <- list(
  num_leaves = 2^6) # maximum number of leaves per tree; controls the maximum complexity of each tree (along with max_depth); more leaves = more expressive models, but can overfit if min_data_in_leaf is too small; num_leaves must be consistent with max_depth, because deeper trees naturally support more leaves; max is: 2^n, where n is the largest max_depth

gp_model_qb <- gpboost::GPModel(
  group_data = data_train_qb_matrix[,"gsis_id"],
  likelihood = model_likelihood,
  group_rand_coef_data = cbind(
    data_train_qb_matrix[,"ageCentered20"],
    data_train_qb_matrix[,"ageCentered20Quadratic"]),
  ind_effect_group_rand_coef = c(1,1))

gp_data_qb <- gpboost::gpb.Dataset(
  data = data_train_qb_matrix[,pred_vars_qb],
  categorical_feature = pred_vars_qb_categorical,
  label = data_train_qb_matrix[,"fantasyPoints_lag"]) #use mean-centered variable and add mean back afterward

# Find optimal tuning parameters
opt_params_qb <- gpboost::gpb.grid.search.tune.parameters(
  param_grid = param_grid_qb,
  params = other_params_qb,
  num_try_random = NULL,
  folds = folds_qb,
  data = gp_data_qb,
  gp_model = gp_model_qb,
  nrounds = nrounds,
  early_stopping_rounds = 50, # stops training early if the model hasn’t improved on the validation set in 50 rounds; prevents overfitting and saves time
  verbose_eval = 1,
  metric = "mae")

Error in fd$booster$update(fobj = fobj): [GPBoost] [Fatal] Inf occured in gradient wrt covariance / auxiliary parameter number 3 (counting starts at 1, total nb. par. = 4) 

opt_params_qb

Error: object 'opt_params_qb' not found

A learning rate of 1 is very high for boosting. Even if a learning rate of 1 did well in tuning, I use a lower learning rate (0.1) to avoid overfitting. I also added some light regularization (lambda_l2) for better generalization. I also set the maximum tree depth (max_depth) at 5 to capture complex (up to 5-way) interactions, and set the maximum number of terminal nodes (num_leaves) per tree at 2^5 (32). I set the minimum number of samples in any leaf (min_data_in_leaf) to be 10.

19.7.7.5 Specify Model and Tuning Parameters

gp_model_qb <- gpboost::GPModel(
  group_data = data_train_qb_matrix[,"gsis_id"],
  likelihood = model_likelihood,
  group_rand_coef_data = cbind(
    data_train_qb_matrix[,"ageCentered20"],
    data_train_qb_matrix[,"ageCentered20Quadratic"]),
  ind_effect_group_rand_coef = c(1,1))

gp_data_qb <- gpboost::gpb.Dataset(
  data = data_train_qb_matrix[,pred_vars_qb],
  categorical_feature = pred_vars_qb_categorical,
  label = data_train_qb_matrix[,"fantasyPoints_lag"])

params_qb <- list(
  learning_rate = 0.1,
  max_depth = 5,
  min_data_in_leaf = 10,
  lambda_l2 = 1,
  num_leaves = 2^5,
  num_threads = num_cores)

nrounds_qb <- 123 # identify optimal number of trees through iteration and cross-validation

#gp_model_qb$set_optim_params(params = list(optimizer_cov = "nelder_mead")) # to speed up model estimation

19.7.7.6 Fit Model

gp_model_fit_qb <- gpboost::gpb.train(
  data = gp_data_qb,
  gp_model = gp_model_qb,
  nrounds = nrounds_qb,
  params = params_qb) # verbose = 0

[GPBoost] [Info] Total Bins 8709
[GPBoost] [Info] Number of data points in the train set: 1582, number of used features: 73
[GPBoost] [Info] [GPBoost with gamma likelihood]: initscore=4.805531
[GPBoost] [Info] Start training from score 4.805531

19.7.7.7 Model Results

summary(gp_model_qb) # estimated random effects model

=====================================================
Covariance parameters (random effects):
                       Param.
Group_1                     0
Group_1_rand_coef_nb_1      0
Group_1_rand_coef_nb_2      0
-----------------------------------------------------
Additional parameters:
      Param.
shape 0.8186
=====================================================

gp_model_qb_importance <- gpboost::gpb.importance(gp_model_fit_qb)
gp_model_qb_importance

gpboost::gpb.plot.importance(gp_model_qb_importance)

Figure 19.1: Importance of Features (Predictors) in Tree Boosting Machine Learning Model.

19.7.7.8 Evaluate Accuracy of Model on Test Data

# Test Model on Test Data
pred_test_qb <- predict(
  gp_model_fit_qb,
  data = data_test_qb_matrix[,pred_vars_qb],
  group_data_pred = data_test_qb_matrix[,"gsis_id"],
  group_rand_coef_data_pred = cbind(
    data_test_qb_matrix[,"ageCentered20"],
    data_test_qb_matrix[,"ageCentered20Quadratic"]),
  predict_var = FALSE,
  pred_latent = FALSE)

y_pred_test_qb <- pred_test_qb[["response_mean"]] # if outcome is mean-centered, add mean(data_train_qb_matrix[,"fantasyPoints_lag"])
cbind(y_pred_test_qb, data_test_qb_matrix[,"fantasyPoints_lag"])

       y_pred_test_qb       
  [1,]     128.741634 156.46
  [2,]      76.493276 130.18
  [3,]      86.580329   2.98
  [4,]      41.918362  24.84
  [5,]      37.188389  40.28
  [6,]      62.495377  10.58
  [7,]      30.746033   0.68
  [8,]      30.473020  25.08
  [9,]      20.828998   6.12
 [10,]      23.109539  17.00
 [11,]      26.812862  44.54
 [12,]      93.304585 152.30
 [13,]     130.223705  -0.10
 [14,]      22.283134 137.96
 [15,]     138.734733 154.78
 [16,]      60.712951   7.64
 [17,]      19.925267   6.10
 [18,]      33.678771 228.66
 [19,]     141.631493 207.44
 [20,]     165.852806  23.80
 [21,]      20.096552 263.06
 [22,]     185.340278 157.30
 [23,]     108.823427 174.48
 [24,]      93.108431 228.56
 [25,]     132.100496  75.36
 [26,]      32.774043   6.72
 [27,]     116.525878  75.06
 [28,]      70.197255 173.40
 [29,]     102.169202 161.88
 [30,]     136.977511  81.36
 [31,]      54.650312  19.86
 [32,]      43.255479  74.86
 [33,]      43.985011  48.92
 [34,]      23.006372  97.48
 [35,]      11.824330  32.84
 [36,]      20.115555  -0.40
 [37,]      73.908501 121.84
 [38,]      83.489164 197.76
 [39,]     102.369357   3.16
 [40,]      20.873240 104.68
 [41,]      44.745490  31.94
 [42,]      34.736537   4.06
 [43,]      14.407108   7.22
 [44,]     159.000821 350.52
 [45,]     241.187535 313.92
 [46,]     236.021580 259.06
 [47,]     222.324392 240.26
 [48,]      94.955165 123.14
 [49,]      80.164614  48.58
 [50,]      17.991425 103.06
 [51,]      58.973741 167.20
 [52,]      61.609967 175.58
 [53,]      59.976242  -0.20
 [54,]      29.445815  71.82
 [55,]     160.600030 244.56
 [56,]     204.093650 156.12
 [57,]     139.802683 222.18
 [58,]      35.005865  17.78
 [59,]      36.632469   1.54
 [60,]      30.553265 134.74
 [61,]      60.602463 182.74
 [62,]     120.450158 177.76
 [63,]      69.612526  14.66
 [64,]      28.041788  19.84
 [65,]      35.010957 150.30
 [66,]      22.786721  44.56
 [67,]      15.690009  40.26
 [68,]      15.229177  86.84
 [69,]      36.787024   5.46
 [70,]      27.012087  43.82
 [71,]     110.714314 303.70
 [72,]     254.844284 271.52
 [73,]     161.540020 235.56
 [74,]     158.224152 230.12
 [75,]     183.533516 310.10
 [76,]     161.558170 165.78
 [77,]     100.085016 201.68
 [78,]     118.356555 219.56
 [79,]     139.661832 255.66
 [80,]     209.394948 248.32
 [81,]     151.262323 193.18
 [82,]      78.426242  66.94
 [83,]      42.375312  44.54
 [84,]      28.387321  11.04
 [85,]      34.347125  67.98
 [86,]      28.271807   6.12
 [87,]      27.680009  12.52
 [88,]      16.829451  -0.20
 [89,]      42.286710  46.68
 [90,]      37.455094  -0.10
 [91,]      14.209401   9.26
 [92,]      29.607459  -0.06
 [93,]      16.339439   2.30
 [94,]      34.811580  75.88
 [95,]      45.060393 157.64
 [96,]     101.488236 218.42
 [97,]     136.011993 204.38
 [98,]     107.216360 178.82
 [99,]      90.485180 275.06
[100,]     116.542558 225.24
[101,]     120.004808 118.96
[102,]      57.158901  49.64
[103,]       8.450484  26.64
[104,]      40.680689  -0.10
[105,]      19.214051  18.02
[106,]      48.741939  35.82
[107,]      16.904948  -0.30
[108,]      37.288545  76.02
[109,]      38.168828   5.48
[110,]      54.013795   3.18
[111,]      39.121789 279.60
[112,]      11.259368  41.64
[113,]      68.275002 194.00
[114,]     121.789308 254.06
[115,]     154.077686  95.30
[116,]      72.317248 117.72
[117,]      69.504155  -0.10
[118,]      18.462864   3.00
[119,]      23.616444  25.82
[120,]      17.513915   2.68
[121,]      28.164915 115.54
[122,]      68.235021   0.20
[123,]      18.903275  -4.64
[124,]      19.013920  41.90
[125,]      37.628651   8.78
[126,]      40.910949 222.70
[127,]     151.389005 144.26
[128,]     113.212570 172.02
[129,]     137.332751  33.90
[130,]      23.393890 185.88
[131,]     100.050362 108.84
[132,]      46.834228 222.92
[133,]     137.834042  17.22
[134,]      29.570081   0.76
[135,]      15.108938   5.90
[136,]      25.744891   2.54
[137,]      22.627555  17.28
[138,]      11.101676  58.24
[139,]      25.133056 123.26
[140,]      66.157443  38.48
[141,]      13.568220  44.22
[142,]      44.336495  17.06
[143,]      25.996324   9.30
[144,]      14.510194   0.70
[145,]      31.883328  -0.30
[146,]      29.645612  11.16
[147,]      31.273725   7.86
[148,]      34.925507   5.62
[149,]      13.326815   1.26
[150,]      21.673501   3.12
[151,]      40.479096   0.02
[152,]      17.576464  51.52
[153,]      20.460485   0.66
[154,]      31.332930  80.12
[155,]      77.812542 156.14
[156,]      83.831779 103.18
[157,]      48.154191   3.50
[158,]      22.053486  86.94
[159,]      50.214249  -0.30
[160,]      22.118031   0.08
[161,]      23.073409  29.36
[162,]      60.378236 142.06
[163,]     122.367750 145.94
[164,]      67.252332 145.16
[165,]      71.689948  64.10
[166,]      28.294902 225.44
[167,]      57.008572  20.76
[168,]      40.510295   0.76
[169,]      18.775275  54.90
[170,]      44.524043   1.24
[171,]      25.292591   2.06
[172,]      27.039092 192.06
[173,]      42.881149   7.76
[174,]      32.373232 187.32
[175,]     150.387990 309.64
[176,]     192.397014 226.02
[177,]     152.404369 287.82
[178,]     196.015905  99.10
[179,]      61.859237 293.96
[180,]     197.685344 289.92
[181,]     198.362766 270.92
[182,]     161.876427 279.30
[183,]     181.418160  44.66
[184,]      32.246875   5.16
[185,]      53.026051   1.36
[186,]      26.739021  18.52
[187,]      24.259145   9.80
[188,]      45.619990 108.18
[189,]      14.431000  49.40
[190,]      45.116690  13.42
[191,]      16.549057 116.84
[192,]      69.821631 190.52
[193,]      93.082768 287.90
[194,]     181.951315 254.60
[195,]     161.991503 162.06
[196,]      63.900804 227.82
[197,]     140.313895 106.80
[198,]      58.216676   0.28
[199,]      32.436363  26.60
[200,]      23.917479   0.44
[201,]      17.931825   3.10
[202,]      12.186139  34.90
[203,]      38.300863  -0.40
[204,]      32.765254  20.94
[205,]      52.356832 228.48
[206,]     172.229067 193.86
[207,]     170.008860 208.34
[208,]     136.565427 202.52
[209,]     178.976431 249.34
[210,]     162.131195 245.08
[211,]     149.237032 294.82
[212,]     186.556782 238.92
[213,]     182.396547 176.32
[214,]     125.736532 277.50
[215,]     183.736196 303.38
[216,]     204.266926 232.18
[217,]     130.324223 207.32
[218,]     116.184853 252.96
[219,]     126.498297  57.38
[220,]      37.905933   7.78
[221,]      27.988110  10.96
[222,]      39.777551  22.32
[223,]      42.225725  68.06
[224,]      34.000295   1.50
[225,]      41.074557   0.08
[226,]      13.086861   5.20
[227,]      54.205994   7.14
[228,]      17.262576  -0.30
[229,]      15.169934  -0.40
[230,]      22.623265  11.40
[231,]      27.822707  14.52
[232,]      77.307391 183.14
[233,]     148.687232  46.46
[234,]      40.627936 148.50
[235,]     100.288020 138.80
[236,]     107.636519 224.66
[237,]     146.200980 128.68
[238,]      98.121358 263.22
[239,]     198.657426 228.00
[240,]     156.993125 277.24
[241,]     246.329016 238.78
[242,]     124.613120 305.18
[243,]     220.580058 147.00
[244,]      91.016938  75.58
[245,]      30.149301  11.04
[246,]      97.815396  30.08
[247,]      29.615726  13.06
[248,]      29.862823  10.80
[249,]      42.880602   6.18
[250,]      18.582752   2.60
[251,]      39.426320   0.36
[252,]      27.081655  40.58
[253,]      41.598284  17.22
[254,]      26.737657  -0.50
[255,]      21.471966  91.04
[256,]      50.240367   4.10
[257,]      45.432195   9.38
[258,]      27.146822  25.36
[259,]      22.802989  -2.04
[260,]      14.182438  46.14
[261,]      29.418591  71.48
[262,]      48.597351 105.70
[263,]      57.581424  88.76
[264,]      37.806320  86.30
[265,]      25.979047   8.66
[266,]      23.473261  60.50
[267,]      37.602489  95.74
[268,]      59.322552  -0.14
[269,]      26.926310   9.38
[270,]      33.732360  51.46
[271,]      32.902369  21.24
[272,]      36.290456 165.66
[273,]     131.064442  67.36
[274,]      33.637376  24.64
[275,]      20.878873   0.56
[276,]      14.406049  56.74
[277,]      26.377241 228.62
[278,]      97.597109   3.62
[279,]      31.198526  30.70
[280,]      38.089529  -0.20
[281,]      13.702492   1.10
[282,]      16.897648   0.64
[283,]      24.109093   6.34
[284,]      15.291694   3.32
[285,]      27.099736  68.88
[286,]      12.289169  16.50
[287,]      40.306380  11.36
[288,]      30.811033   1.54
[289,]      21.187629   6.08
[290,]      36.854653   0.58
[291,]       9.586886  15.80
[292,]      20.288053  40.20
[293,]      47.787870 163.94
[294,]      88.311608 172.64
[295,]     105.607589  86.60
[296,]      37.185148  68.88
[297,]      41.158467  -0.52
[298,]      18.341251  23.08
[299,]      31.616863   4.00
[300,]      31.711285  12.28
[301,]      34.345689   1.48
[302,]      23.597819   4.94
[303,]      33.000776  10.36
[304,]     124.891067 277.44
[305,]     276.204245 222.08
[306,]     133.652128 254.50
[307,]     193.993233  32.44
[308,]      40.784760  10.36
[309,]      23.957448  26.08
[310,]      33.239390  14.08
[311,]      41.439719  90.80
[312,]      10.741727   4.14
[313,]      23.364617   0.64
[314,]      40.466157  15.82
[315,]      22.240615  35.16
[316,]      27.247508   8.72
[317,]      24.145373   1.36
[318,]      16.520377  -0.06
[319,]      52.035577  52.34
[320,]      42.698605  -0.10
[321,]      20.081118  10.30
[322,]      16.811510   3.60
[323,]       5.731763   7.40
[324,]      46.571609   7.30
[325,]      15.133207  10.80
[326,]      28.142495   6.30
[327,]      26.298198   1.00
[328,]      29.664469  19.64
[329,]     131.687161 105.16
[330,]      50.415712 238.48
[331,]     192.839895 122.58
[332,]      83.087206 209.90
[333,]     158.465827 237.88
[334,]     158.802879  26.98
[335,]      28.543762  16.70
[336,]      25.201194 184.74
[337,]     294.399300 335.46
[338,]     286.936554 303.66
[339,]     283.207946 266.98
[340,]     194.034487 402.08
[341,]     284.085081 261.26
[342,]     184.420419 308.98
[343,]     235.617287 284.60
[344,]     254.053458  21.68
[345,]      48.701302 268.98
[346,]     154.391063  90.36
[347,]      39.677908 151.42
[348,]      85.958124 142.14
[349,]     147.934323 103.74
[350,]      73.762001  69.92
[351,]      29.167055  14.52
[352,]      37.297271 182.06
[353,]     154.307424 277.28
[354,]     246.460310 266.66
[355,]     212.461996 116.20
[356,]      68.500815 213.44
[357,]     127.057103 103.92
[358,]      35.410808   7.42
[359,]      17.959288   3.52
[360,]      11.116868   0.56
[361,]      17.493820  24.80
[362,]      10.795376  43.02
[363,]      33.196895 150.30
[364,]      19.024410   1.76
[365,]      24.762455  21.44
[366,]      37.343413  24.48
[367,]      36.697686   6.32
[368,]      43.181861  54.44
[369,]      20.101485   0.04
[370,]      16.767578  64.58
[371,]     125.986092  93.64
[372,]      36.723727  20.02
[373,]      49.948221  68.42
[374,]      49.353231  -0.10
[375,]      28.406756  30.32
[376,]     134.429972 256.32
[377,]     165.478621 294.50
[378,]     197.385257 278.32
[379,]     197.815050 202.20
[380,]     151.141117 151.96
[381,]      68.605926 234.18
[382,]     108.453988 352.36
[383,]     228.238143 280.86
[384,]     213.589369 167.24
[385,]     118.522178  85.04
[386,]      39.168380  -0.20
[387,]      40.377452   0.72
[388,]      20.339467  -1.46
[389,]      66.706760   6.46
[390,]      34.642560  11.68
[391,]      22.835408   1.70
[392,]      20.856311  30.32
[393,]      23.503427   0.76
[394,]       7.723413   6.72
[395,]      26.252434  12.16
[396,]      18.913424  19.40
[397,]      22.684451   0.00
[398,]      18.947548  14.52
[399,]      22.801240 102.00
[400,]      94.982190 122.04
[401,]      12.241181 196.74
[402,]     113.067567 132.10
[403,]      50.474916   0.12
[404,]      16.840156  94.16
[405,]      41.287889  10.16
[406,]      21.782455  34.96
[407,]      23.833366   8.56
[408,]      25.434350  -0.48
[409,]      83.461217  18.80
[410,]      38.138719  28.00
[411,]     189.927323  17.98
[412,]      50.768424  -3.24
[413,]      20.242938   1.80
[414,]      14.520171  -1.90
[415,]      21.928831  16.80
[416,]      16.346178   0.38
[417,]      12.478261   0.00
[418,]      38.724728  26.02
[419,]      18.810524   8.78
[420,]      12.306305   0.20

petersenlab::accuracyOverall(
  predicted = y_pred_test_qb,
  actual = data_test_qb_matrix[,"fantasyPoints_lag"],
  dropUndefined = TRUE
)

19.7.7.9 Generate Predictions for Next Season

# Generate model predictions for next season
pred_nextYear_qb <- predict(
  gp_model_fit_qb,
  data = newData_qb_matrix[,pred_vars_qb],
  group_data_pred = newData_qb_matrix[,"gsis_id"],
  group_rand_coef_data_pred = cbind(
    newData_qb_matrix[,"ageCentered20"],
    newData_qb_matrix[,"ageCentered20Quadratic"]),
  predict_var = FALSE,
  pred_latent = FALSE)

newData_qb$fantasyPoints_lag <- pred_nextYear_qb$response_mean

# Merge with player names
newData_qb <- left_join(
  newData_qb,
  nfl_playerIDs %>% select(gsis_id, name),
  by = "gsis_id"
)

newData_qb %>% 
  arrange(-fantasyPoints_lag) %>% 
  select(name, fantasyPoints_lag, fantasyPoints)

19.8 Conclusion

19.9 Session Info

sessionInfo()

R version 4.5.1 (2025-06-13)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.2 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
 [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
 [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
[10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   

time zone: UTC
tzcode source: system (glibc)

attached base packages:
[1] parallel  stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] lubridate_1.9.4   forcats_1.0.0     stringr_1.5.1     dplyr_1.1.4      
 [5] purrr_1.0.4       readr_2.1.5       tidyr_1.3.1       tibble_3.3.0     
 [9] tidyverse_2.0.0   gpboost_1.5.8     R6_2.6.1          caret_7.0-1      
[13] lattice_0.22-7    ggplot2_3.5.2     powerjoin_0.1.0   missRanger_2.6.1 
[17] doParallel_1.0.17 iterators_1.0.14  foreach_1.5.2     petersenlab_1.1.5

loaded via a namespace (and not attached):
 [1] DBI_1.2.3            mnormt_2.1.1         pROC_1.18.5         
 [4] gridExtra_2.3        rlang_1.1.6          magrittr_2.0.3      
 [7] compiler_4.5.1       vctrs_0.6.5          reshape2_1.4.4      
[10] quadprog_1.5-8       pkgconfig_2.0.3      fastmap_1.2.0       
[13] backports_1.5.0      pbivnorm_0.6.0       rmarkdown_2.29      
[16] prodlim_2025.04.28   tzdb_0.5.0           xfun_0.52           
[19] jsonlite_2.0.0       recipes_1.3.1        psych_2.5.6         
[22] lavaan_0.6-19        cluster_2.1.8.1      stringi_1.8.7       
[25] RColorBrewer_1.1-3   ranger_0.17.0        parallelly_1.45.0   
[28] rpart_4.1.24         Rcpp_1.0.14          knitr_1.50          
[31] future.apply_1.20.0  base64enc_0.1-3      FNN_1.1.4.1         
[34] Matrix_1.7-3         splines_4.5.1        nnet_7.3-20         
[37] timechange_0.3.0     tidyselect_1.2.1     rstudioapi_0.17.1   
[40] yaml_2.3.10          timeDate_4041.110    codetools_0.2-20    
[43] listenv_0.9.1        plyr_1.8.9           withr_3.0.2         
[46] evaluate_1.0.4       foreign_0.8-90       future_1.58.0       
[49] survival_3.8-3       pillar_1.10.2        checkmate_2.3.2     
[52] stats4_4.5.1         generics_0.1.4       mix_1.0-13          
[55] hms_1.1.3            scales_1.4.0         globals_0.18.0      
[58] xtable_1.8-4         class_7.3-23         glue_1.8.0          
[61] Hmisc_5.2-3          tools_4.5.1          data.table_1.17.6   
[64] ModelMetrics_1.2.2.2 gower_1.0.2          mvtnorm_1.3-3       
[67] grid_4.5.1           mitools_2.4          ipred_0.9-15        
[70] colorspace_2.1-1     nlme_3.1-168         RJSONIO_2.0.0       
[73] htmlTable_2.4.3      Formula_1.2-5        cli_3.6.5           
[76] viridisLite_0.4.2    lava_1.8.1           gtable_0.3.6        
[79] digest_0.6.37        htmlwidgets_1.6.4    farver_2.1.2        
[82] htmltools_0.5.8.1    lifecycle_1.0.4      hardhat_1.4.1       
[85] MASS_7.3-65         

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